J∇TO: Joint Nabla Tracking Optimizer

J∇TO (Joint Nabla Tracking Optimizer) is a unified framework for multi-target tracking that integrates statistical gating via Mahalanobis distance, rigid association (Hungarian) via negative likelihood cost, joint probabilistic association (JPDA) with JPDAF update, unified association operator Aτ interpolating Hungarian↔JPDA with anti-switch temporal prior, IMM–Kalman filter, and probabilistic M/N management. It includes statistical consistency, clutter modeling, out-of-order measurements (OOSM), and online calibration of λc and λB. The result is a stable and mathematically coherent framework applicable to highly complex multi-sensor tracking systems.